PSY 311 1st Edition Lecture 12Outline of Last Lecture I. One way design II. Assignment of participants III. Posttest designIV. Pretest posttest design V. Factorial design VI. Nomenclature VII. Assignment of participants VIII. Main effects IX. Combined effects a. Additivityb. Non-additivityOutline of Current Lecture I. Why are multiple t-test a problem? II. When to use Analysis of Variance III. The F-statistic IV. The logic of ANOVA V. What is our measure of variability? VI. Notation and formulas VII. Last notational glitchVIII. F- distribution Current LectureI. Why are multiple t-test a problem?- Pairwise type 1 error (αp)- Comparing two groups when you conduct a t-test - Experimentwise type 1 error (αe)- Across the entire experiment II. When to use analysis of variance (anova)- 2 Groups t-test or Anova- Equivalent tests!!!- More than 2 groups Must use AnovaIII. The F-statistic - Recall that the t statistic is the difference between means divided by difference expected by chance- Because difference cannot be calculated with more than 2 groups, we use variance - Thus, F statistic is the variance between means divided by variance expected by chance IV. The logic of anova• Between-treatment variance– Differences between the means– Due to treatment AND chance• Within-treatment variance– Differences within groups– Because all participants are in the same condition, difference are dueONLY to chanceV. What is our measure of variability?• Sum of Squares!!!!SStotal = SSbetween + SSwithindftotal = dfbetween + dfwithin– SStotalis the sum of squares if you combine all the data; dftotal = N - 1(N is total sample size)– SSbetween is the sum of squares for the sample means; dfbetween = k - 1 (k is numberof conditions)– SSwithin is the sum of squares within each condition (add them all up!); dfwithin = N- kVI. Notation and formulas G= Grand total , N= Total sample , T= group totalVII. Last notational glitch Variance is also called the mean square (MS) MSbetween = SSbetween / dfbetween MSwithin = SSwithin / dfwithin F = MSbetween / MSwithinVIII. F-Distribution - If the null hypothesis is ture, then the ration follows f
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